Three in 10 respondents would rather not think about getting older at all. Only a quarter predict it’s very likely they will need help getting around or caring for themselves, according to the poll, done by the AP-NORC Center for Public Affairs Research.

That’s a surprise, considering more than half of the 40-plus people polled have been caregivers for an impaired relative or friend — seeing from the other side the kind of assistance they, too, are likely to need later on.

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Bowman has been a caregiver twice, first for her grandmother. Then after her father died in 2006, Bowman moved in with her mother, caring for her until her death in January. Yet Bowman has made few plans for herself.

The poll found most respondents expect family to step up if they need long-term care — even though 6 in 10 haven’t talked with loved ones about the possibility and how they’d like it to work.

Bowman said she expects to need help someday from her two grown sons. Last month, prompted by a brother’s fall and blood clot, she began the conversation by telling her youngest son about her living will and life insurance policy.

Family conversations are crucial: Even if they want to help, do your relatives have the time, money, and know-how? Can they afford to hire help? What if you no longer can live alone?

‘‘The expectation that your family is going to be there when you need them often doesn’t mean they understand the full extent of what the job of caregiving will be,’’ said Susan Reinhard, a nurse who directs AARP’s Public Policy Institute. ‘‘Your survey is pointing out a problem for not just people approaching the need for long-term care, but for family members.”

Government figures show nearly 7 in 10 Americans will need long-term care at some point after age 65, whether from a relative, home health aide, assisted living, or a nursing home. On average, they’ll need care for three years.

Despite the ‘‘it won’t happen to me’’ reaction, the poll found half of those surveyed think just about everyone will need assistance at some point. There are widespread misperceptions about how much care costs and who will pay for it. Nearly 60 percent of those surveyed underestimated the average cost of a nursing home, more than $6,700 a month.

Medicare doesn’t pay for the most common types of long-term care. Yet 37 percent of those surveyed mistakenly think it will pay for a nursing home and even more expect it to cover a home health aide when that’s only approved under certain conditions.

Medicaid, the federal-state program for the poor, is the main payer of long-term care, and to qualify seniors must have spent most of their savings and ­assets.

But fewer than half of those polled think they’ll ever need Medicaid — even though only a third are setting aside money for later care.

The poll found widespread support for tax breaks to encourage saving for long-term care, and about half favor the government establishing a voluntary long-term care insurance program. An Obama administration attempt to create such a program ended in 2011 because it was too costly.

Just 8 percent of 40- to 54-year-olds have done much planning for long-term care, compared with 30 percent of those 65 or older, the poll found.

The AP-NORC Center for Public Affairs Research survey was conducted Feb. 21 through March 27, with funding from the SCAN Foundation.

The nonprofit foundation supports research and other initiatives on aging and health care.

The poll involved landline and cellphone interviews with 1,019 Americans 40 or older. Its margin of error is plus or minus 4.1 percentage points.